Chapter ISG, Problem 6.2.4P

To determine

To write a system of equation and find value.

Answer to Problem 6.2.4P

AC=6.8 centimetres

AB=8.5 centimetres

Explanation of Solution

Given information:

A triangle with perimeter 24.3 centimetres.

Formula used: perimeter of triangle

Calculation:

Length of BC= 9cm

Let length of AB and AC be x and y respectively,

Using perimeter of triangle,

Sum of all sides= perimeter

AB+BC+CA=23.4 cm

Substituting values,

  $b+9+c=24.3$

Solving,

  $b+c=24.3-9$

So,

  $b+c=15.3$

Also, ratio of $b:c=4:5$

Let the lines be 4x and 5x respectively,

  $4x+5x=15.3$

Solving equation,

  $9x=15.3$

So,

  $x=1.7$

Length is:

b = $4x=4(1.7)=6.8$

c = $5x=5(1.7)=8.5$